{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:L3ME7BHK6WKM7VPD2HS4GW4SXY","short_pith_number":"pith:L3ME7BHK","canonical_record":{"source":{"id":"2505.21738","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-27T20:28:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a385571477278541c178d88b5cd721b30720913bf5ed0195d6b572506b479160","abstract_canon_sha256":"15bc3410f46a721b9f596874c5f53f9ada9882d3f317199d6bb3a6ad9bc2c00c"},"schema_version":"1.0"},"canonical_sha256":"5ed84f84eaf594cfd5e3d1e5c35b92be1931fa5abdffd568dd86635cdd5e7887","source":{"kind":"arxiv","id":"2505.21738","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21738","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21738v1","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21738","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"L3ME7BHK6WKM","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"L3ME7BHK6WKM7VPD","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"L3ME7BHK","created_at":"2026-07-05T11:11:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:L3ME7BHK6WKM7VPD2HS4GW4SXY","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21738","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-27T20:28:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a385571477278541c178d88b5cd721b30720913bf5ed0195d6b572506b479160","abstract_canon_sha256":"15bc3410f46a721b9f596874c5f53f9ada9882d3f317199d6bb3a6ad9bc2c00c"},"schema_version":"1.0"},"canonical_sha256":"5ed84f84eaf594cfd5e3d1e5c35b92be1931fa5abdffd568dd86635cdd5e7887","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:02.726206Z","signature_b64":"/klpwgZ0RaLd4zGv9EuKx3ka1W4BPyHCzQ4q5n7WiBMH3hVhZXZVhcqSkpCa00o7tfjEOc+89zK1xtg8gUm5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ed84f84eaf594cfd5e3d1e5c35b92be1931fa5abdffd568dd86635cdd5e7887","last_reissued_at":"2026-07-05T11:11:02.725771Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:02.725771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21738","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPTjRy0pPBUS5FljEqeQVauCd5Tql+aMe9/F1CygCGrbURCfbOYLgH2cLWquofQkm+9I/CtG3lhhd6r4Eu28BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:36:26.762908Z"},"content_sha256":"455ca51019a576a101a6c32c678f312f55dfa883f80dd2760895c1825c736a83","schema_version":"1.0","event_id":"sha256:455ca51019a576a101a6c32c678f312f55dfa883f80dd2760895c1825c736a83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:L3ME7BHK6WKM7VPD2HS4GW4SXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic Branching through Crystals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"B\\'arbara Muniz","submitted_at":"2025-05-27T20:28:13Z","abstract_excerpt":"We give an alternative proof of Naito--Sagaki's conjecture, which states that the restriction of $gl_{2n}(\\mathbb{C})$-representations to $sp_{2n}(\\mathbb{C})$ can be described in terms of crystals. Using the tableau model for crystals, we construct an explicit and self-contained bijection between their highest weight elements and Sundaram's branching model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21738","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQtsHOKylI/qDS0YddqBcfnwfUHNIkEZV83rpgJENRrSzuHycK3/okKnISu5twMT26yvM9TNebouoh0JQX9DDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:36:26.763415Z"},"content_sha256":"4124df0a06f8cef27ed434be168b288cb8915e8b8c877a8fa1a8cc733755a769","schema_version":"1.0","event_id":"sha256:4124df0a06f8cef27ed434be168b288cb8915e8b8c877a8fa1a8cc733755a769"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/bundle.json","state_url":"https://pith.science/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T09:36:26Z","links":{"resolver":"https://pith.science/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY","bundle":"https://pith.science/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/bundle.json","state":"https://pith.science/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L3ME7BHK6WKM7VPD2HS4GW4SXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:L3ME7BHK6WKM7VPD2HS4GW4SXY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"15bc3410f46a721b9f596874c5f53f9ada9882d3f317199d6bb3a6ad9bc2c00c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-27T20:28:13Z","title_canon_sha256":"a385571477278541c178d88b5cd721b30720913bf5ed0195d6b572506b479160"},"schema_version":"1.0","source":{"id":"2505.21738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21738","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21738v1","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21738","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_12","alias_value":"L3ME7BHK6WKM","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_16","alias_value":"L3ME7BHK6WKM7VPD","created_at":"2026-07-05T11:11:02Z"},{"alias_kind":"pith_short_8","alias_value":"L3ME7BHK","created_at":"2026-07-05T11:11:02Z"}],"graph_snapshots":[{"event_id":"sha256:4124df0a06f8cef27ed434be168b288cb8915e8b8c877a8fa1a8cc733755a769","target":"graph","created_at":"2026-07-05T11:11:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.21738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an alternative proof of Naito--Sagaki's conjecture, which states that the restriction of $gl_{2n}(\\mathbb{C})$-representations to $sp_{2n}(\\mathbb{C})$ can be described in terms of crystals. Using the tableau model for crystals, we construct an explicit and self-contained bijection between their highest weight elements and Sundaram's branching model.","authors_text":"B\\'arbara Muniz","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-27T20:28:13Z","title":"Symplectic Branching through Crystals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21738","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:455ca51019a576a101a6c32c678f312f55dfa883f80dd2760895c1825c736a83","target":"record","created_at":"2026-07-05T11:11:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"15bc3410f46a721b9f596874c5f53f9ada9882d3f317199d6bb3a6ad9bc2c00c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.RT","submitted_at":"2025-05-27T20:28:13Z","title_canon_sha256":"a385571477278541c178d88b5cd721b30720913bf5ed0195d6b572506b479160"},"schema_version":"1.0","source":{"id":"2505.21738","kind":"arxiv","version":1}},"canonical_sha256":"5ed84f84eaf594cfd5e3d1e5c35b92be1931fa5abdffd568dd86635cdd5e7887","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ed84f84eaf594cfd5e3d1e5c35b92be1931fa5abdffd568dd86635cdd5e7887","first_computed_at":"2026-07-05T11:11:02.725771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:02.725771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/klpwgZ0RaLd4zGv9EuKx3ka1W4BPyHCzQ4q5n7WiBMH3hVhZXZVhcqSkpCa00o7tfjEOc+89zK1xtg8gUm5Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:02.726206Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455ca51019a576a101a6c32c678f312f55dfa883f80dd2760895c1825c736a83","sha256:4124df0a06f8cef27ed434be168b288cb8915e8b8c877a8fa1a8cc733755a769"],"state_sha256":"9506af4e314072258b7cb8f0199bdf1e2f9bb105127209560ccd040376cf76f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r8Bgr6Xb+8bZqWAUHqgP3LouUnFYrPhf2Xewy5TVa6YZo67/i0NoqExzkCsTSZzfa5e8TDEyvMrlmAfdCXhhCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:36:26.768111Z","bundle_sha256":"9ed22c65d38d0b8ae97bec4f84e42bd2fac93b5f5c5d9bf0a53c8f9932707728"}}